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In the given figure find the ratio of sum of inradius and circumradius for smaller triangle and bigger triangle, if the side of smaller equilateral triangle is 25% of the side of bigger equilateral triangle ?
- a)2 : 3
- b)1 : 4
- c)4 : 7
- d)8 : 3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In the given figure find the ratio of sum of inradius and circumradiu...
Given
Side of smaller equilateral triangle = 25% side of bigger equilateral triangle
Formula used:1) Circumradius = abc/4Δ
2) Inradius = Δ/s
Where, s = (a + b + c)/2
And Δ = Area of triangle
3) Area of equilateral triangle = √3/4 × a2
Calculation:According to question,
Side of smaller equilateral triangle = 25% side of bigger equilateral triangle
Side of smaller equilateral triangle/Side of bigger equilateral triangle = ¼
Sum of circumradius and inradius for smaller triangle,
⇒ 1 × 1 × 1/4 × √3/4 × (1)2 + √3/4 × (1)2/(1 + 1 + 1)/2
⇒ 1/√3 + 1/2√3
⇒ 1/√3 × (1 + 1/2)
⇒ 3/2√3
Similarly,
Sum of circumradius and inradius for bigger triangle,
⇒ 4 × 4 × 4/ 4 × √3/4 × (4)2 + √3/4 × (4)2/ (4 + 4 + 4)/2
⇒ 4/√3 + 2√3/3
⇒ 4/√3 + 2/√3
⇒ 6/√3
Ratio = 3/2√3 : 6√3
⇒ 3/2 : 6
⇒ 3 : 12
⇒ 1 : 4
∴ The correct answer is 1 : 4.
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In the given figure find the ratio of sum of inradius and circumradius for smaller triangle and bigger triangle, if the side of smaller equilateral triangle is 25% of the side of bigger equilateral triangle ?a)2 : 3b)1 : 4c)4 : 7d)8 : 3Correct answer is option 'B'. Can you explain this answer?
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